Finite Group Databasebeta

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C2×#14544932 #17970587

order4352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#14544932
unambiguous semidirect productD17⋊#1971

Splittings

FittingC22×Q16×C17 ⋊ C4
SylowC17 ⋊ C2×#1971

Subgroups

subgroupG/H
centerC23D4×#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC22×Q16×C17C4
socleC23×C17C4×D4
prime radicalC23×D17C2×D4
cosocleC2×C4×D17C24
hypercenterC22×Q16#595
hypocenterC17C2×#1971
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

1574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1105831);